Uncertainty of weekly nitrate-nitrogen forecasts using artificial neural networks

Nonpoint source pollution affects the quality of numerous watersheds in the Midwestern United States. The Illinois State Water Survey conducted this study to (1) assess the potential of artificial neural networks (ANNs) in forecasting weekly nitrate-nitrogen (nitrate-N) concentration; and (2) evaluate the uncertainty associated with those forecasts. Three ANN models were applied to predict weekly nitrate-N concentrations in the Sangamon River near Decatur, Illinois, based on past weekly precipitation, air temperature, discharge, and past nitrate-N concentrations. Those ANN models were more accurate than the linear regression models having the same inputs and output. Uncertainty of the ANN models was further expressed through the entropy principle, as defined in the information theory. Using several inputs in an ANN-based forecasting model reduced the uncertainty expressed through the marginal entropy of weekly nitrate-N concentrations. The uncertainty of predictions was expressed as conditional entropy of future nitrate concentrations for given past precipitation, temperature, discharge, and nitrate-N concentration. In general, the uncertainty of predictions decreased with model complexity. Including additional input variables produced more accurate predictions. However, using the previous weekly data (week t-1) did not reduce the uncertainty in the predictions of future nitrate concentrations (week t+1) based on current weekly data (week t).